Cities Growth Page

Summary

Do foraging animals and growing cities utilize resources in the same way? We're interested in building an agent-based model which generates a road network on a map of varying resources by following a set of simple, probabilistic rules. How do the properties of this network evolve through time? How much of city growth can be explained by resource constraints? Do simple rules of growth parallel simple rules of animal foraging behavior? This project will explore agent-based modeling, but will also present opportunities to examine the limits of modeling.

Objectives - Research Question(s)

Road networks are an integral part of city infrastructure, but the drivers of their structure and evolution are not well understood. At the most basic level, we posit that road networks are a means of searching out and transporting resources important for human activity. Other animals also exhibit this searching or foraging behavior. In this project, we will use the analogy of foraging animals to model the development of road networks in cities. Here we will ask how much of the structure of city road networks can be explained by a searching procedure like that of a foraging animal.

Our work will build on previous literature on foraging and city scaling, but will depart from this in two ways. We will develop an agent-based model that builds on simpler models of foraging in the literature but includes varied topography in the search space. We will also build on studies of the structure of city road networks by developing a mechanistic model that can be tested empirically against real city networks, both past and present. If validated, the model may have implications for understanding the development of road networks in new cities, or the expansion of existing cities.

This project involves a number of steps, not necessarily to be completed in this exact order:

1. Define essential properties of city networks, which will be used to evaluate the performance of the model.

2. Examine these properties in candidate animal foraging routes. What are the similarities and differences?

3. Develop an agent-based model of animal foraging on a landscape with varied resources and terrain, to be applied to city networks. What features of the model (e.g. network persistence) should be adapted from the foraging to the city case? What are the parallels?

4. Run the model using a relatively simple map, and evaluate the network properties determined to be important. Select a method for measuring these properties.

5. Run the model using a real-world map (for example, the city of Santa Fe), and compare the results visually to the actual map.

Groups Members

Alberto
Alex (brummera@email.arizona.edu
Bernardo (bernardo.furtado@ipea.gov.br)
Claire (lagesse.claire at gmail.com)
Diana (dianalg11@gmail.com)
Ernest Liu (yu.liu@math.uu.se)
James
Michael Kalyuzhny (michael.kalyuzhny at mail.huji.ac.il)
Morgan (morgane@mit.edu)
Rohan (rsmehta at stanford dot edu)

Meetings

Tuesday 17 : 3:00 pm - 5:00 pm
4:15 p.m. - 4:25 p.m. : Meeting with Josh

Wednesday 18 : 9:00 am - 12:00 am

---

done :

Thursday 12 : 6:00 pm - 7:00 pm
Monday 16 : 2:30 pm - 4:15 pm

Ongoing work

• Create a wiki page ! (Claire) [OK]

• Write the research question (Morgan) [OK]

Literature

• Find more references (Claire [OK] & Rohan [OK])
• Overview of NetLogo models libraries (Ernest)
• Overview of Aaron's model (Rohan [OK])
• Overview of Alfred's experiment model (Alex)
• Overview of Slime mold model (Michael & Ernest)

Data

• List & Upload data on the Dropbox (Claire)
• Historical Maps of Santa Fe (Alex)

Foraging perspective

• Think about the processes we want to model (Diana & Michael)
• List relevant animals to study (James, Diana & Michael)

Modelling First Step

• Think about the models which could be relevant (Ernest, Claire, Bernardo, Alberto, Morgan, Rohan)

>> Let's write a little paragraph for each model we have in mind

References

• Bernardo

File:Quick Literature Review on Growth of Cities.pdf

• Claire

Growing Artificial Societies
Turtles, Termites, and Traffic Jams
There's also "Artificial Ants" (Nicolas Monmarché) but I can't find a free article about his computation. That's a shame because I remember of a really interesting algorithm with a well done exploration / exploitation balance...

Overviews

Slime mold

[1]

Processes

Foraging processes we want to observe

Scale-free foraging patterns are currently a hot topic in animal movement biology. Typically, these scale-free patterns are identified through time series data - how far does the animal move before it changes direction? Are these step lengths drawn from a power law distribution? It is unique to consider foraging in a network context. However, one might hypothesize that a network formed through a scale-free search pattern might also be scale-free. It would also be interesting to note how properties unique to foragers but not to cities (like having to return to a home or nest, or not creating permanent roads) change the shape of a foraging network.

Models

Rohan's proposition

Here's my idea for a network model. We start out with a grid (fine, but still a grid; a continuous map may be too computationally intensive), with each cell possessing some attributes: elevation, proximity to resources, and proximity to roads. We choose a root at random (or not) and add nodes by the following process: within the field of view (an NxN square surrounding each node), choose the cell whose edge has minimum cost. The cost is determined by taking into account the following values: the effective length of the proposed edge (factoring in topography), the length of the path from the root to the proposed node, (from the Gastner and Newman paper), the proximity of the new node to the nearest resource, and the proximity of the node to existing roads (the closer it is to existing roads, the less we need to make it a node in the road network). The resource proximity part should be a function of population density: the greater the population/the smaller the resource budget of the population, the more heavily weighted this part. If the resource budget is sufficient (this will only be temporary), no node is added; we can ignore these steps since nothing happens. The foraging model will be the exact same model except roads are not built on the network; the network still exists as a set of repeated movement patterns, but there are no roads, and so the proximity-to-roads part of the cost function has weight 0. Foraging animals probably do not use their much-traveled paths to go anywhere other than the end of the path. If the resource budget situation is dire and there are no really useful cells in the field of view, there is an option to jump to a random location that is nearby but outside the field of view and add the resulting patch to the field of view. Of course, in most cases such a jump would result in fairly long proposed edges, which would be costly, but hopefully the benefit of landing near a resource outweighs the cost. The jumps can have a distance from the field of view drawn from a heavy-tailed distribution.